AbstractLet Bm be the mth Bernoulli number in the even suffix notation and let q(a, n)=(aϕ(n)−1)/n be the Fermat–Euler quotient, where a, n⩾2 are relatively prime positive integers and ϕ is the Euler totient function. The main purpose of this paper is to devise a certain congruence involving the Bernoulli number and Fermat–Euler quotient, which leads to several important arithmetic properties of Bernoulli numbers
AbstractFor m>n≥0 and 1≤d≤m, it is shown that the q-Euler number E2m(q) is congruent to qm−nE2n(q)mo...
Fermat’s and Euler’s theorem on congruencies are generalized to the case when the integers a and m a...
We consider some congruences involving arithmetical functions. For example, we study the congruences...
AbstractLet [x] be the integral part of x. Let p>5 be a prime. In the paper we mainly determine ∑x=1...
For a Dirichlet character χ modulo M, the generalized Bernoulli num-bers Bm,χ ∈ Q(χ(1), χ(2),...) (m...
AbstractLet {Bn(x)} be the Bernoulli polynomials. In the paper we establish some congruences for Bj(...
Let χ denote a primitive quadratic character mod M (or the trivial character) and let d be a fundame...
AbstractLet Bm be the mth Bernoulli number in the even suffix notation and let q(a, n)=(aϕ(n)−1)/n b...
The study of class number invariants of absolute abelian fields, the investigation of congruences fo...
AbstractMany of the classical theorems for the Bernoulli numbers, particularly those congruences nee...
AbstractLet {Bn(x)} denote Bernoulli polynomials. In this paper we generalize Kummer's congruences b...
Let p be a prime greater than or equal to 5: In this paper, by usingthe harmonic numbers and Fermat ...
AbstractIn 1935, Carlitz introduced analogues of Bernoulli numbers for Fq[t]. These are now called B...
AbstractIf we denote Bn to be nth Bernoulli number, then the classical result of Adams (J. Reine Ang...
AbstractWe extend Euler's well-known quadratic recurrence relation for Bernoulli numbers, which can ...
AbstractFor m>n≥0 and 1≤d≤m, it is shown that the q-Euler number E2m(q) is congruent to qm−nE2n(q)mo...
Fermat’s and Euler’s theorem on congruencies are generalized to the case when the integers a and m a...
We consider some congruences involving arithmetical functions. For example, we study the congruences...
AbstractLet [x] be the integral part of x. Let p>5 be a prime. In the paper we mainly determine ∑x=1...
For a Dirichlet character χ modulo M, the generalized Bernoulli num-bers Bm,χ ∈ Q(χ(1), χ(2),...) (m...
AbstractLet {Bn(x)} be the Bernoulli polynomials. In the paper we establish some congruences for Bj(...
Let χ denote a primitive quadratic character mod M (or the trivial character) and let d be a fundame...
AbstractLet Bm be the mth Bernoulli number in the even suffix notation and let q(a, n)=(aϕ(n)−1)/n b...
The study of class number invariants of absolute abelian fields, the investigation of congruences fo...
AbstractMany of the classical theorems for the Bernoulli numbers, particularly those congruences nee...
AbstractLet {Bn(x)} denote Bernoulli polynomials. In this paper we generalize Kummer's congruences b...
Let p be a prime greater than or equal to 5: In this paper, by usingthe harmonic numbers and Fermat ...
AbstractIn 1935, Carlitz introduced analogues of Bernoulli numbers for Fq[t]. These are now called B...
AbstractIf we denote Bn to be nth Bernoulli number, then the classical result of Adams (J. Reine Ang...
AbstractWe extend Euler's well-known quadratic recurrence relation for Bernoulli numbers, which can ...
AbstractFor m>n≥0 and 1≤d≤m, it is shown that the q-Euler number E2m(q) is congruent to qm−nE2n(q)mo...
Fermat’s and Euler’s theorem on congruencies are generalized to the case when the integers a and m a...
We consider some congruences involving arithmetical functions. For example, we study the congruences...
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